Defect Prediction in Composites Based on Numerical Simulation and - - PDF document

18TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS

Defect Prediction in Composites Based on Numerical Simulation and Expertise Knowledge

Li YanXia*, LI Min, GU Yi-Zhuo, Sun Jing and ZHANG Zuo-Guang Key Laboratory of Aerospace Materials and Performance (Ministry of Education), Beihang University, Beijing, 100191, P R China

* Corresponding author (liyanxia@buaa.edu.cn)

Keywords: Carbon fiber composite, manufacture, defects, void

Abstract Advanced composites components for aircraft application continues to rise and primary structures are increasingly made from advanced composites. The quality and its stability of the composites structure are very important. As we known, the composites structure is formed together with the composite material. The material, processes and design practices that are used to generate the composite structure will affect the quality. It is necessary to develop a method being able to previously predict the defect in the composites and to improve the quality of the composites material. In this paper, based on the numerical simulation module (temperature and pressure field prediction including the auxiliary material and composites) and expertise knowledge i.e. combined with statistical results and defect micrographs, the strong correlation between geometric characteristics (for instance, thickness, curvature radius) in composite components and controllability of manufacturing defects was obtained, the void defect can be predicted for the L-shaped laminates. These results can provide a good reference for the processor and designer, and are very helpful for the improvement and quality control of composite parts. 1 Introduction Advanced composites are commonly used as structural components in aircraft, aerospace, and automotive industries. Autoclave molding technology is one of the most popular techniques for these materials. However, during the manufacturing process of composites components, various defects such as void, delamination and debonding, etc., inevitably appear as results of curing schedule, environment, raw materials, and unreasonable structure design of composite components. These manufacturing defects sometimes cause serious threat to mechanical properties and service life of composites, paralleled with making a great economic loss. Exploring the causes and controlled methods of defects in composites has attracted increasing consideration over the past few decades. The types of composite components applied to aircraft are different and complex; therefore, the resin flow of composite components is much more complicated because of the complexity of temperature distribution and pressure transfer in

• components. In more detail, the ratio of defect

appearance would increase and the controllability of such defects would also become difficult when some structure parameters exceed a certain range. In this paper, Numerical models were developed and simulations were conducted for composites to study the temperature and pressure in the laminates during the cure process. Combined with the model of pore growth and the expertise knowledge (experimental data), the probability of generation of pore in the laminate can be predicted. These results can provide a good reference for the processor and designer, and are very helpful for the improvement and quality control of composite parts. 2 Process Model 2.1 Temperature Field For the heat transfer in composites during the autoclave process, the governing equations combined the heat transfer and resin reaction kinetics is established, which is responsible for calculation of the distribution of component temperature and the cure degree of resin. For the two-dimensional case, and with the coordinate axes aligned with the material principal axes, heat transfer equation can be written as:

p xx zz

T T T C k k t x x z z ρ ρ ∂ ∂ ∂ ∂ ∂ ⎛ ⎞ ⎛ ⎞ = + + ⎜ ⎟ ⎜ ⎟ ∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ &

RH

(1)

Where T is the temperature, t is the time; ρ and Cp are the composite density and specific heat capacity, respectively. kxx and kzz are the thermal conductivities, ρR is the resin density, H

& is the rate of

heat generation of the resin exothermic reaction. Coordinate z refers to the thickness direction of the laminate while x refers to the length direction. At

each step, a variety of equations are used to calculate the composite thermo-physical properties in Eq.1 from the local fiber volume fraction, and instantaneous resin and fiber properties. The rate of heat generation in Eq.1 can be determined from:

u u ( , )

da H H H f T dt α = = & (2)

Where Hu is the total amount of heat generated during a ‘complete’ resin reaction, a is the degree of cure, da/dt is cure rate and is a function of temperature T and degree of cure a. For the tool and auxiliary materials, the Fourier heat transfer model is used, the material property parameters including thermal conductivity, heat specific, density obtained by experiments. 2.2 Pressure Field The squeezed sponge model was employed to describe the resin flow and fiber compaction behavior in composite. The composite material is assumed to be an elastic, deformable, porous medium in which the resin flows relative to the fiber bed obeying Darcy’s law. For the representative element, the differential equilibrium equation can be written as:

ij j i

P x x σ ∂ ∂ + = ∂ ∂

(3)

Where σij and P are the fiber effective stress and resin pressure, respectively. Subscript i and j stand for Cartesian coordinates x or z. According to the mass conservation, the flow continuity equation is expressed as:

v xx zz

S S P P t x x z z ε µ µ ∂ ⎛ ⎞ ⎛ ∂ ∂ ∂ ∂ = + ⎜ ⎟ ⎜ ∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎞ ⎟ ⎠

(4)

Where Sxx, Szz are the fiber bed permeability which varies with varying fiber volume fraction, µ is resin viscosity, εv is the bulk strain. The simplified constitutive equation [3, 11-12] is

( ) ( )

xx xx xx 4 zz f a f xz xz xz

s 1 / 1 E A V V V V G σ ε σ τ γ = = ⋅ − − =

(5)

where Exx, Ezz and Gxz are the fiber bundle elastic constants, εxx, εzz and γxz are the strains, Vf is the fiber volume fraction, Va is the maximum available fiber volume fraction, V0 is the initial fiber volume fraction, As is a spring constant. The finite element formulations and validations

• f the flow-compaction model can be found in Ref.

[2]. Resin viscosity, fiber bed permeability and fiber volume fraction are updated at each time step in the solution. 3 Manufacturing Defects in Autoclave Molding In reference [3], the manufacturing defects were summarized systematically according to the results of non-destructive identification such as ultrasonic and X-ray, in which some defects of fiber waviness, fiber volume fraction non uniformity, and thickness non-uniformity were not included in the statistical range. The main defects often formed in autoclave molding and the defect ratio between the number of every type of defects and the number of total defects are presented in Figure 1. The statistical data sample for various types of manufacturing defects distributed in every compo- site component is listed in table 1. In Fig.1 and Table 1, D1, D2, D3, D4, D5, D6, D7, and D8 refers to delamination, void, pore, debonding, rich resin, lack resin, loose, and deform- ation, respectively.A1 and A2 in Table 1 represent the total number of components with defects and total number of components.

10 20 30 40 50 D1

D2 D8 D3 D4 D5 D6 D7 Defect type Defect ratio(% )

Fig.1 Contrast graph for manufacturing defects

• Table1. Statistical data sample of manufacturing defects

in composite components

From Fig.1, obviously, delamination occupies a dominant position among the manufacturing defects; pore and void are also two important defects of which ratios are much lower than delamination ratio but higher than the other defect ratios. Curvature radius is a typical geometric charac- teristic of composite components, which are widely applied in beams, webs, and stiffened plates. The effect of different curvature radius on manufacturing

Defect Prediction in Composites Based on Numerical Simulation and Expertise Knowledge

defects and contrast for defect types in the curve zone are shown in Fig.2 and Fig.3, respectively. It can be seen from Fig.2 that the defect ratio gradually decreases and the controllability of these defects increases with increasing the curvature radius of

• components. From Fig.3, the maximum ratio of

defects in curve zone is delamination, the second maximum ratio of defects is void and loose, and the effect of curvature radius on rich resin and lack resin is the weakest. Fig.4 showed the metallograph of void in the corner region.

• Fig2. Effect of curvature radius on manufacturing defects
• Fig3. Contrast graph for various defects in curve zone
• Fig4. Void defect in the corner

4 Defects prediction in L-shaped Composites From the experimental result, voids are one of the main types of manufacturing defects, while the negative impact of voids on laminates has been largely studied, and it has been shown that voids can promote damages, crack initiation and propagation and these defects generate important mechanical property decreases like interlaminar shear stress, tensile strengths, and modulus of elasticity [4, 5]. Therefore, it is mandatory to minimize the

• ccurrence and growth of these porosities in

composite laminates, phenomenon that can be directly linked to manufacturing process. The mainly source of voids can summarized as air entrapped in the lay-up assembly and volatile small molecule such as water and dissolvent in the

• resin. While the temperatures, resin pressure, vapour

pressure in the pore, the time of pressure application and gel time are the main factors effecting the void formation, growth and inhibiting. According to Raoult’s law, for the acetone in the resin solution, we can get the model of pore formulation as:

3 min

3568 5.12 10 exp

r

P P X T − ⎛ ⎞ ≥ = × ⎜ ⎟ ⎝ ⎠

(6)

In which, Pr is resin pressure; Pmin is the minimum pressure to inhibiting the growth of pore; X0 is mole fraction of acetone in the resin. Based on the GPC method, with the molecular weight of resin, acetone, resin volume fraction and volatile content, the mole fraction of acetone in the resin solution can be calculated. For the air entrapped in the lay-up, the following model is gotten to describe the pore growth.

2 4 min

3568 5.84 10 exp 3.41 10 0.10

r

P P T T

−

− ⎛ ⎞ ≥ = × + × − ⎜ ⎟ ⎝ ⎠

(7)

With the numerical simulation models, the temperature and pressure in the composite laminates can be predicted, combined with the model of pore growth and the expertise knowledge (experimental data), the probability of generation of pore in the laminate can be predicted. FEA method and self-developed program are developed to solve the numerical simulation models and predict the temperature and pressure distribution in the composite laminates during the curing process. With the numerical models, the material properties i.e. material systems, lay-up type, cure cycles (temperature, pressure, and the time of pressure application) and structure parameters (thickness, radiu, etc.) can be studied. It is an effective method to predict the defects produced in the curing process. 4.1 temperature prediction Firstly, based on the heat transfer models, the effect of rubber mould on heat transfer was studied with the configuration as shown in Fig.5 including the aluminum tool, the L-shaped lay-up, bleeder materials and rubber mould. All the boundaries are set as the convective boundary with h=130W/m2·K.

3

The gas temperature in the autoclave was increased from room temperature to 120 ℃ and then the temperature was held for 10min. After that, the temperature was raised to 190℃ and then kept at this temperature for 30min. Fig.6 was the temperature difference between the typical points in the lay-up assembly including the auxiliary materials. During the cure cycle, the maximum temperature difference is about 9℃ in the rubber mould and 3℃ in the lay-up, respectively. According to the simulated results, for the thin laminates, the temperature distribution is uniform and the effect of temperature difference on the consolidation process can be ignored in the following study.

Fig.5 Schematic for heat transfer analysis

2000 4000 6000 8000

• 2
• 1

1 2 3 4 5

Temperature difference/K time/second

temperature=P2-P1 temperature=P3-P2 temperature=P7-P2

(a) Temperature difference in the lay-up

2000 4000 6000 8000

• 2

2 4 6 8 10

Temperature difference/K time/second

temperature=P6-P4 temperature=P5-P4

(b) Temperature difference in the rubber mould Fig.6 temperature difference between the typical points

4.2 pressure prediction

• Fig. 7 shows a schematic of manufacturing an L-

shaped laminate. In this study, the influence of tool- part interaction on the pressure transfer of tools and the consolidation process of laminates before resin gelation are considered in the numerical model. Fig.8. 4-node elements were used for the whole

• model. The symmetrical arm lengths of L-shaped

laminate and metal die were 50mm and 80mm, respectively.

• Fig. 7 Schematic of manufacturing an L-shaped laminate

and a sliding interface condition occurs at the tool-part interfaces

• Fig. 8 Geometry and mesh for the simulation
• Fig. 9 shows the resin pressure distribution in the

laminates, with the different radius. From the results, we can find that the resin pressure in the corner region is much lower than the one in the flat part and the smaller the radius is, lower is the resin pressure in the corner. The regular is similar to the experimental results. Base on the simulation mode, the model of pore growth and expertise knowledge, probability distribution of void in the laminate can be predicted in Fig.10. The pore is easier to formulate in the corner, which is corresponding to the experimental data and approve the valuation of prediction method of defects.

(a) R=4mm (b) R=10mm

• Fig. 9 Resin pressure distribution

Defect Prediction in Composites Based on Numerical Simulation and Expertise Knowledge Fig.10 Predicted probability distribution of void

References

[1] Li YX. “Numerical Simulation and Processing Analysis of Resin Flow and Fiber Bed Compaction of Advanced Composites”. PhD Thesis, Beihang University; 2008. [2] Li M, Li YX, Zhang ZG, Gu YZ. “Numerical Simulation

• f

Two-Dimensional Flow and Compaction during the Consolidation of Laminated Composites”. Polymer. Composites, No.10, pp560- 568, 2008. [3] X.M Wang, Z.G. Zhang, F.Y. Xie, et al “Correlated Rules between Complex Structure of Composite Components and Manufacturing Defects in Autoclave Molding Technology”. Journal of Reinforced Plastics and Composites, 2008. [4] Chambers A.R., Earl J.S., Squires C.A., et al. “The effect of voids on the flexural fatigue performance of unidirectional carbon fiber composites developed for wind turbine applications”. International Journal of Fatigue, Vol.28, No.10, pp1389-1398, 2006. [5] Almeida SFM, Neto ZSN. “Effect of void content on the strength of composite laminates”. Composite Structure, Vol.28, No.2, pp139-148, 1994. [6] J. Sun, Y.Z Gu, Y.X Li et al.“Role of tool-part interaction in consolidation of L-shaped laminates during autoclave process”.Composites: PartA, submitted. 5